Question: Multiply the following complex numbers: $({-i}) \cdot ({-4-5i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-i}) \cdot ({-4-5i}) = $ $ ({0} \cdot {-4}) + ({0} \cdot {-5}i) + ({-1}i \cdot {-4}) + ({-1}i \cdot {-5}i) $ Then simplify the terms: $ (0) + (0i) + (4i) + (5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 4)i + 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 4)i - 5 $ The result is simplified: $ (0 - 5) + (4i) = -5+4i $